Evaluation of a two-stage evaporation approximation for contrasting vegetation cover

For a regional assessment of water needs and consumption in semiarid agricultural zones, one needs robust and simple tools that provide space-time estimates of evaporation losses. Most operational evaporation estimates rely on semiempirical relationships that are not generally applicable. Several authors have proposed physically based simple expressions to model the "energy-limited'' (stage-one) and the "supply-limited'' (stage-two) evaporation rates during a dry down. They use the time compression approximation (TCA) to relate stage-one and stage-two drying. Two asymptotic approximations of the TCA corresponding to the diffusion-dominated and the drainage-dominated flows have been proposed in the literature. In this study a full analytical solution of the TCA is presented. The derived "supply-limited'' evaporation rate is evaluated for a wide range of soil conditions and vegetation cover against a physically based complex soil-vegetation-atmosphere transfer model, the Simple Soil-Plant-Atmosphere Transfer scheme (SiSPAT). SiSPAT solves the differential equations of water flow in a vertical soil column and computes estimates of soil evaporation and transpiration. SiSPAT is used to evaluate the performance of the full solution as well as the two existing asymptotic approximations for the case of sparse to dense vegetation in a semiarid environment. The full analytical solution gives accurate predictions of first- to second-stage evaporation time series for the bare soil and vegetated cover conditions with a leaf area index of 3 or higher. The results of the full solution are closer to the evaporation rate time series simulated by SISPAT than the asymptotic approximations.